Appendix E
Direct-Product Tables
Extensive direct-product tables are provided by Herzberg [10]. Antisymmetrized
and symmetrized parts of direct squares are indicated by braces and brackets, respectively.
D 3
A 1
A 2
E
A 1
A 1
A 2
E
A 2
A 2
A 1
E
EEE[A 1 + E]+{A 2 }
D 4
A 1
A 2
B 1
B 2
E
A 1
A 1
A 2
B 1
B 2
E
A 2
A 2
A 1
B 2
B 1
E
B 1
B 1
B 2
A 1
A 2
E
B 2
B 2
B 1
A 2
A 1
E
EEEEE[A 1 + B 1 + B 2 ]+{A 2 }
D 5
A 1
A 2
E 1
E 2
A 1
A 1
A 2
E 1
E 2
A 2
A 2
A 1
E 1
E 2
E 1
E 1
E 1
[A 1 + E 2 ]+{A 2 }
E 1 + E 2
E 2
E 2
E 2
E 1 + E 2
[A 1 + E 1 ]+{A 2 }
D 6
A 1
A 2
B 1
B 2
E 1
E 2
A 1
A 1
A 2
B 1
B 2
E 1
E 2
A 2
A 2
A 1
B 2
B 1
E 1
E 2
B 1
B 1
B 2
A 1
A 2
E 2
E 1
B 2
B 2
B 1
A 2
A 1
E 2
E 1
E 1
E 1
E 1
E 2
E 2
[A 1 + E 2 ]+{A 2 }
B 1 + B 2 + E 1
E 2
E 2
E 2
E 1
E 1
B 1 + B 2 + E 1
[A 1 + E 2 ]+{A 2 }
A.J. Ceulemans, Group Theory Applied to Chemistry, Theoretical Chemistry and
Computational Modelling, DOI 10.1007/978-94-007-6863-5,
© Springer Science+Business Media Dordrecht 2013
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